Question: Multiply the following complex numbers: $({-1-4i}) \cdot ({-4-4i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-4i}) \cdot ({-4-4i}) = $ $ ({-1} \cdot {-4}) + ({-1} \cdot {-4}i) + ({-4}i \cdot {-4}) + ({-4}i \cdot {-4}i) $ Then simplify the terms: $ (4) + (4i) + (16i) + (16 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (4 + 16)i + 16i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (4 + 16)i - 16 $ The result is simplified: $ (4 - 16) + (20i) = -12+20i $